Feasibility of Using Backscattered Light to Recover Refractive Index Gradient in Biological Samples (Crystalline lens)PAYMAN RAJAISupervised byDr. REJEAN MUNGERVisual Optics Lab, University of Ottawa Eye InstituteOttawa Hospital Research Institute

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The Customized Eye Model

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• Future is more personalized medicine• Personalized correction of refraction

– Wavefront very good but still some issues– Next step to further improve outcomes is usingpersonalized optical model of the eye for designingoptimal refractive correction

• Diagnosis of vision loss– Separation of optical vs. retinal causes– Separate corneal vs. lenticular problems

Limitation to building personal eye models: Crystalline lens

The Crystalline Lens: A Complex Optical Component

Photo from: http://www.chinaphar.comIndex at the surface ≈ 1.386 Index at the center ≈ 1.406

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Non symmetric biconvex oblate spheroid

The Problem

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• The shape of the gradient is still unknown• This is the main unanswered question to be able to build customized eye models• No reliable direct or indirect measurements have everbeen done. Current average models are not validated,and no one else has attempted personalized lensmodels

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Previous Studies in our Lab:Ray Tracing Approach

Apply GRIN MODEL with fitting parameters to reproduce the optical properties

Cynthia Wilson Thesis 2010, Visual Optics Lab, University of Ottawa Eye Institute

Problem with ray tracing approach

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• Difficult to do ray tracing measurements inside an eye• This is a model. If it is not the realphysiological GRIN, it will likely break downwhen applied to real life, for exampleduring accommodation, when the lenschanges its focus.

Direct model validation is needed

The Goal of my ProjectTo determine if the data available incommercial optical coherence tomography(OCT) systems is sufficient to reconstruct thecrystalline lens GRIN

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Detector GRIN Measurement ??!!

Reference Arm

Benefits of the Project

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• Enabling measurement in clinical situations– Build customized eye models for each patient forbetter diagnostics and treatment planning

• Solution has general problem of measuring therefractive index in inhomogeneous materialswith high transparency

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Detector

Movable reference mirror in TD-OCT

Weakly scattering object

δ - like layers interfaces

Beam splitter

TD-OCT FD-OCT

Short Coherence Source

Basic Principles of OCT

OCT – Crystalline Lens Challenge• Applied to retina • Applied to lens

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very thinLayers, continuously varying index

Index =n, thickness = AIndex =n, thickness = BIndex =n, thickness = C

Index =na, thickness = AIndex =nb, thickness = BIndex =nc, thickness = CIndex =nd, thickness = DIndex =ne, thickness = E

The math behind the current OCT analysis is not sufficient to solve for the GRIN in the lens.

Approaches Considered to Solve OCT for the Inhomogeneous Refractive Index

• Plane Wave Approach (Bottom up)• Diffraction Tomography Approach(Top down)

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Plane Wave Approach(bottom up)

Z1Z2Z3

n1n2n3

Incident waveReflected waves from different layers

Round trip optical path

Z1, Z2, Z3 = different thicknesses n1, n2, n3 = different refractive indices

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Coupled index-position

Possible Solutions

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• Oblique illumination at two different angles– We have developed the problem using two beams, incident at different angles– Found that this method does allow us to decouple the index and position in the lens– Not a classic implementation of OCT, would need new device

• Multiple wavelength equivalent to FD-OCT type approach – Early result show that it is highly probable but we have not found the full solution yet (IN PROGRESS)

• Two short coherence length sources with different spectra or different central wavelengths (IN PROGRESS)

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Diffraction Tomography Approach(Top down)

Weakly scattering object

Incident plane waves Transmitted light contains information about the sample

We can recover the object if we have

enough detected dataOCT is a special case of DT

Inverse Scattering Problem

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Born Approximation

Rytov Approximation

Born approximation is valid only for almost transparent or thin samples

Rytov approximation is valid for smooth fluctuations of light

Direct application to OCT

The source power spectrum

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If the sample is compatible with the Born approximation:

Detected intensity free from DC and AC termsInverse Fourier TransformObject Function (scattering potential)

Direct application to the OCT

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If the sample is compatible with the Rytov approximation

Detected intensity free from DC and AC termsInverse Fourier TransformObject Function (scattering potential)

CONCLUSION• We have developed three promising methods to find the GRIN of the crystalline lens based on OCT data• These include the oblique illumination approach, the multi-wavelength approach, and the diffraction tomography approach• Future work includes experimental determination of which approach is the best to find the GRIN of the lens

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Acknowledgment

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Many thanks to Dr. Munger for hisguidance, Zack Dube and Luisa Lee fortheir help with animations and textpreparation

THANK YOU

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